@SteveCostenoble : Is there any internal Kunneth formula for integer graded Bredon cohomology theory , i.e. We know the integer graded Bredon cohomology of $G$-spaces $X ,Y$ respectively and we wanted to know about the Bredon cohomology of $X \times Y$ ?

@SteveCostenoble : I know the explicit $Z/6$-CW($\xi^2$)-complex structure of $D(\xi^2)$ . I am looking for an explicit calculation for $Z/6$-CW($\xi^2$)-complex structure of $D(2\xi^2)$ .it'll be great if you kindly calculate the explicit (geometric) structure of it.

@SteveCostenoble:We know that $S(V+W)= S(V)*S(W)$.Now I know the $Z/6$ CW complex structures of $S(\xi^2)$ and $S(2\sigma)$.How can I compute the attaching maps for $S(\xi^2 + 2\sigma)$?

@SteveCostenoble: Thank you very much.You are such an inspiration for me.

@SteveCostenoble : Thank you for your valuable comment.I had read most of the papers of Gaunce Lewis and Jeff Caruso(just One paper).But I never saw any paper on the calculation $H^*_{G}(*,M)$ for $|G| = p^n$.It will be nice if you can find it for me.I have another question that'll help me for the above calculation.Question:What is $Z/6$-complex structure of $S(\xi + \xi^2 + 2\sigma)$ ? Where $\xi$ ,$\xi^2$ are defined in above comment and $\sigma$ is 1 real dimensional sign representation of $Z/6$.

@SteveCostenoble: Thank you very much for your comment.I am interested in $ G = Z/6 $, $ M = Z/6$-constant Mackey functor and $\alpha = \xi^2 - \xi$, where $\xi$- is nontrivial irreducible representation of $Z/6$ with out fixed point.Is it possible to find $i^*$ in this setting?

@ White: I can't able to understand the cofiber property of "Equivariant euler chracteristics".Can you give me any rigorous and lucid proof?

:could you please do this problem using the contractions of bredon cohomology made in J.P.May's Equivariant Homotopy and Cohomology Theory Book at pages 20-21?